Leishman moved to 6 under for the day through 16 holes and at that point was within one of leader Kevin Tway who was out in the second group of the day and put together an opening round of 66 on the par 73 layout to take the early lead.
He hit his tee shot on the par-3 second hole to 2 feet, followed that with a wedge to 10 feet for birdie on the next hole and really never came close to a bogey.
"The thing is if I can get through that front nine in under par there is good chances on the back nine and that is what I did out there today", McIlroy added.
Tway is the son of eight time US PGA Tour victor and major champion Bob and travelled with his father to Maui for the winners-only event in 2004.
Kevin Tway earned a one-stroke lead after the opening round at the Tournament of Champions as the 2019 PGA Tour season got underway.
The Tour's winners-only event in Maui welcomes only those players who have notched victories during the 2018 calendar year.More news: Injuries a worry for Sarri as Chelsea beat Palace
Kizzire admitted in one of the new experimental mid-round interviews with the Golf Channel that he was just aiming to get on the green with his shot.
After Leishman's drive on 17, the 35-year-old barely advanced his second shot out of the native area and despite a strong third shot failed to get up and down for bogey. He tried to whack it out and reached only the rough and wound up with a double bogey.
"I stayed patient", McIlroy said.
Defending champion Dustin Johnson was over par for the first time in 33 rounds at Kapalua.
It was the first tournament day where the players experienced the new rules introduced by the R & A and the USGA, with a few players choosing to putt with the flagstick left in, notably Bryson DeChambeau, an advocate of putting with the flag in place, who did it even from close range.
"I played good", Tway said.